Optical characterization of the phosphate glasses containing pair transition ions

The paper deals with optical and electronic properties of the aluminophosphate glasses containing Fe–Mn and Fe–Cr ion pairs in different concentration. The influence of the mixed alkali ions over the electronic properties has been investigated. The optical behavior (optical transmission) of the glass samples has been studied by UV-VIS spectroscopy and the refractive index dependency on wavelength has been discussed. The transmission spectra show features specific for the doping transition ions (TM), revealing different oxidation states of iron (Fe²⁺/Fe³⁺), manganese (Mn²⁺/Mn³⁺) and chromium (Cr³⁺/Cr⁶⁺) in the vitreous network. Mössbauer spectroscopy offers information regarding the TM oxidation states, redox processes and the iron coordination symmetry in the vitreous network. In the case of Fe–Mn doped glasses, the percentage of Fe²⁺ is about 40% and a doubled iron content leads to an increasing of Fe²⁺ percentage up to 53%. The replacing of lithium ions by natrium ions (mixed alkali effect) provides an increasing of the Fe²⁺ percentage up to 56%. The occurrence of the tetrahedral or octahedral symmetry of Fe²⁺ ions bonded by O^2? ions depends on the transition ion nature and Li⁺/Na⁺ ratio. Infrared absorption spectra of the pair transition ions-doped aluminophosphate glasses reveal optical phonons specific for the phosphate glass matrix.     

Adsorption of water on reconstructed rutile TiO2(011)-(2 x 1): Ti=O double bonds and surface reactivity

Recent combined experimental and theoretical studies (Beck et al., Phys. Rev. Lett. 2004, 93, 036104) have provided evidence for Ti=O double-bonded titanyl groups on the reconstructed rutile TiO(2)(011)-(2 x 1) surface. The adsorption of water on the same surface is now investigated to further probe the properties of these groups, as well as to confirm their existence. Ultraviolet photoemission experiments show that water is adsorbed in molecular form at a sample temperature of 110 K. At the same time, the presence of a 3sigma state in the photoemission spectra and work function measurements indicate a significant amount of hydroxyls within the first monolayer of water. At room temperature, scanning tunneling microscopy (STM) suggests that dissociated water is present, and about 30% of the surface active sites are hydroxylated. These findings are well explained by total energy density functional theory calculations and Car-Parrinello molecular dynamics simulations for water adsorption on the titanyl model of TiO(2)(011)-(2 x 1). The theoretical results show that a mixed molecular/dissociative layer is the most stable configuration in the monolayer regime at low temperatures, while complete dissociation takes place at 250 K. The arrangement of the protonated mono-coordinated oxygens in the mixed molecular/dissociated layer is consistent with the observed short-range order of the hydroxyls in the STM images.     

Backward and forward-looking expectations in a chaotic cobweb model

In this study we research the dynamics shown by a cobweb-type model with linear demand, non-invertible supply function and with forward-looking expectations associated to backward looking ones. The study of the dynamics exhibited by our model will show how the presence of forward-looking expectations represents a stabilising factor: As the weight attributed to the above mentioned foreseeing form increases, the system becomes less and less complex until it only generates orbits converging either to the fixed point or to a cycle-2. It is particularly interesting to analyse at the same time the role played by the two forms of expectations considered, both of which contribute to market stabilization.     

Relation between Different Types of Global Attractors of Set-Valued Nonautonomous Dynamical Systems

The article is devoted to the study of the relation between forward and pullback attractors of set-valued nonautonomous dynamical systems (cocycles). Here it is proved that every compact global forward attractor is also a pullback attractor of the set-valued nonautonomous dynamical system. The inverse statement, generally speaking, is not true, but we prove that every global pullback attractor of an α-condensing set-valued cocycle is always a local forward attractor. The obtained general results are applied while studying periodic and homogeneous systems. We give also a new criterion of the absolute asymptotic stability of nonstationary discrete linear inclusions. Dedicated to our friend Professor Enrico Primo Tomasini on the occasion of his 55th birthdayMathematics Subject Classifications (2000) Primary: 34C35, 34D20, 34D40, 34D45, 58F10,58F12, 58F39; secondary: 35B35, 35B40.     

A gould type integral with respect to a multisubmeasure

In [GOULD, G. G.: Integration over vector-valued measures, Proc. London Math. Soc. (3) 15, (1965), 193–205], G. G. Gould introduced a type of integral of a bounded, real valued function with respect to a finite additive set function taking values in a Banach space, integral which is more general than the Lebesgue one. Recently, A. Precupanu and A. Croitoru gave the generalization, defining a Gould type integral for multimeasures with values in _kc(X), X being a Banach space ([PRECUPANU, A.—CROITORU, A.: A Gould type integral with respect to a multimeasure, I, An. Ştiinţ. Univ. “Al. I. Cuza” Iaşi Secţ. I a Mat. 48 (2002), 165–200]). Taking as starting point this work and [PRECUPANU, A.—CROITORU, A.: A Gould type integral with respect to a multimeasure, II, An. Ştiinţ. Univ. “Al. I. Cuza” Iaşi Secţ. I a Mat. 49 (2003), 183–207], we define here the notion of a Gould type integral with respect to a _bf(X)-valued multisubmeasure, pointing out important properties of it. We also establish that, even if we deal with multisubmeasures, the integral is still a multimeasure.      

Maximality of the signless Laplacian energy

We study the problem of determining the graph with $n$ vertices having largest signless Laplacian energy. We conjecture it is the complete split graph whose independent set has (roughly) $2n∕3$ vertices. We show that the conjecture is true for several classes of graphs. In particular, the conjecture holds for the set of all complete split graphs of order $n$, for trees, for unicyclic and bicyclic graphs. We also give conditions on the number of edges, number of cycles and number of small eigenvalues so the graph satisfies the conjecture.     

Expanding measures

We prove that any C1+α transformation, possibly with a (non-flat) critical or singular region, admits an invariant probability measure absolutely continuous with respect to any expanding measure whose Jacobian satisfies a mild distortion condition. This is an extension to arbitrary dimension of a famous theorem of Keller (1990) [33] for maps of the interval with negative Schwarzian derivative.Given a non-uniformly expanding set, we also show how to construct a Markov structure such that any invariant measure defined on this set can be lifted. We used these structure to study decay of correlations and others statistical properties for general expanding measures.     

A compact 341 model at TeV scale

We build a gauge model based on the SU(3)_c⊗SU(4)_L⊗U(1)_X$SU{\left(3\right)}_c\otimes SU{\left(4\right)}_L\otimes U{\left(1\right)}_X$ symmetry where the scalar spectrum needed to generate gauge boson and fermion masses has a smaller scalar content than usually assumed in literature. We compute the running of its abelian gauge coupling and show that a Landau pole shows up at the TeV scale, a fact that we use to consistently implement those fermion masses that are not generated by Yukawa interactions, including neutrino masses. This is appropriately achieved by non renormalizable effective operators, suppressed by the Landau pole scale. Also, SU(3)_c⊗SU(3)_L⊗U(1)_N$SU{\left(3\right)}_c\otimes SU{\left(3\right)}_L\otimes U{\left(1\right)}_N$ models embedded in this gauge structure are bound to be strongly coupled at this same energy scale, contrary to what is generally believed, and neutrino mass generation is rather explained through the same effective operators used in the larger gauge group. Besides, their nice features, as the existence of cold dark matter candidates and the ability to reproduce the observed standard model Higgs-like phenomenology, are automatically inherited by our model. Finally, our results imply that this model is constrained to be observed or discarded soon, since it must be realized at the currently probed energy scale in LHC.